For a real number x, if \(\rm \frac{1}{2}, \frac{\log_3(2^x-9)}{\log_34},\ and\ \frac{\log_5\left(2^x+\frac{17}{2}\right)}{\log_54}\) are in arithmetic progression, then the common difference is
1
\(\rm \log_4\left(\frac{3}{2}\right)\)
2
\(\rm \log_4\left(\frac{23}{2}\right)\)
3
\(\rm \log_4\left(\frac{7}{2}\right)\)
4
log47